1932: US Senator Robert P. Shuler (Prohibition--California)

"Shuler's controversial broadcasts also included attacks on Catholics, African Americans, Jews and on the President of the University of Southern California, for permitting evolution to be taught. During the 1928 Presidential election, with Catholic Alfred E. Smith running as the Democratic candidate, Shuler asserted that the Catholics were "plotting to urder Protestants in their beds."[1] He also publicly defended the Ku Klux Klan.[6][7] In June 1930, the Los Angeles Times published a lengthy feature story about Shuler under the headline: "Champion 'Ag'inner' of Universe Is Shuler: Belligerent Local Pastor Holds All Records for Attacks Upon Everybody, Everything."[8] The Times wrote: "Unless you have been attacked by Rev. 'Bob' Shuler, pastor of Trinity Methodist Church South, via radio, magazine, pulpit or pamphlet (25 cents per copy) you don't amount to much in Los Angeles."[8] Shuler's targets included the Los Angeles Public Library (for carrying books not fit to be read even in "heathen China or anarchistic Russia"), the YWCA (for conducting dances for girls "until the early hours of Sunday morning"), and other evangelists, including Billy Sunday and Aimee Semple McPherson...[In his 1932 Senate campaign] Shuler freely admitted "I don't know what I'll do in Washington until I get there"..." https://en.wikipedia.org/wiki/Robert_P._Shuler

That even Depression-era California could elect somone like this may strain belief, but he got over one-fourth of the vote statewide, http://www.ourcampaigns.com/RaceDetail.html?RaceID=26815 and carried Orange and Riverside Counties. Suppose William McAdoo https://en.wikipedia.org/wiki/William_Gibbs_McAdoo dies a decade early, California Democrats nominate someone less acceptable to "dry" Democrats--or one who if "dry" is controversial for other reasons (say that Upton Sinclair siwtches from Socialist to Denmocrat two years early and wins the Democratic senatorial primary), and Shuler actually wins in a closely contested three-way race in November?...
Assuming he can actually get into the Senate, I imagine he'd be like Huey Long, but somehow even more unpopular among his fellow legislators. I'm not sure if he'd have good relations with the Southern Democrat caucus for his anti-Jew, anti-Black, and anti-Catholic views, or if he'd be seen as too much of a loud, obnoxious demagogue who'd embarrass them.
I doubt he's allowed to caucus with either party, or that his Senate career lasts more than a term. The biggest butterfly I see here is that, with a greater platform, Shuler possibly becomes a third-party candidate for the populist right in '36 or some kind of America-Firster in '40 -- but without other butterflies, probably doesn't swing either election. (I don't know enough about internal Prohibition Party politics at the time to know whether they end up embracing or disowning Shuler -- if the former, than Prohibition's association with a "Fascist" possibly kills them off entirely after WWII, robbing us of OTL's most persistent third party.)